Self-similar cosmological solutions in f(R, T) gravity theory

We study the f(R, T) cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the field equations (FE) admit exact self-similar (SS) solutions through the matter collineation approach. We study two models: the case f(R, T) = f(1)(R) + f(2)(T) and the case f(R, T) = f(1)(R) + f(2)(R)f(3)(T). In each case, we state general theorems which determine completely the form of the unknown functions f(i) such that the FE admit SS solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous SS metric. In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models.